**P. 4563.** A steam funicular railway is to be built to Hill Gellért. The top of the hill is 84 m higher than its foot. The total length of the straight slope is 140 m. There are two cars of equal masses, hung by cables at the two sides of a pulley, and one of them travels uphill whilst the other one travels downhill. In each car 40 people can travel. The funicular is loaded the most when there are 40 people in the car which is travelling up, while the other car is empty. The mass of each car is 5 tons. The average weight of a passanger is 70 kg. The coefficient of rolling friction on the iron rails is 0.005. Calculate the output of the steam engine in horse power, if one trip lasts for one minute. (The stiffness and the mass of the cable, the rotational inertia of the pulley, and air drag can be neglected in this estimation.)

(4 points)

**P. 4566.** A model car of mass *m*=12 kg travels on a horizontal rough surface along a circular path of radius *R*=5 m. It starts from rest and for a while it has a constant tangential acceleration of *a*_{0}=2 m/s^{2}, and when its acceleration reaches the value of , then it continues its motion along the circular path at constant speed.

*a*) Measured from the starting instant, when will the car reach the point at which it started?

*b*) What is the maximum of the static frictional force?

(5 points)